The invention relates generally to positioning systems, more especially, but not exclusively, to a method of and apparatus for finding a signal in a multi-dimensional search space.
Positioning systems are often used to achieve relative alignment between two or more components in such a way that there is maximum coupling efficiency of a signal passing between the components concerned. An example is the coupling of signals into or out of optical fibers. Other examples occur in microscopy, including scanning probe microscopy and electron microscopy where non-optical signals are involved.
Generally, the alignment procedure can be sub-divided into two stages as shown in FIG. 1 of the accompanying drawings. The first step, indicated as S1 in FIG. 1, consists of a coarse alignment to find a signal. The second step, indicated as S2 in FIG. 1, consists of a fine alignment to increase the level of the signal found in step S1 to a maximum, or at least to an acceptably large, level.
Automated procedures for the second step of optimizing the signal once it has been found are commercially available. However, the first step of finding the signal prior to optimization is generally performed by hand with a user moving the positioners into the general vicinity of what can be seen to be the general alignment area for the device concerned while looking at a signal indicator. In fact, the initial coupling to find the signal is in many cases the most time consuming part of the procedure, especially if the second step is automated.
Particular and preferred aspects of the invention are set out in the accompanying independent and dependent claims. Features of the dependent claims may be combined with those of the independent claims as appropriate and in combinations other than those explicitly set out in the claims.
According to the present invention there is thus provided an apparatus for and a method of performing an automated search applicable to finding a signal in a multi-dimensional search space of any number of dimensions. Once found, the signal can then be optimized using standard automated signal optimization procedures.
The automation of the signal location step is achieved by scanning over a search pattern defined by a succession of nxe2x88x921 dimensional hyper-surfaces in an n-dimensional search-space, where n is the number of positioning axes involved in the alignment process.
The search space is a hyper-space, where n may assume any positive integer value such that n greater than =4. By the same token, the search surfaces of dimensionality nxe2x88x921 will be hyper-surfaces, i.e. surfaces of dimensionality of three or more. The word surface is used here in a general sense. If there is a search space of n-dimensions, the surface will be topologically equivalent to a sphere, cube, or whatever other shape is selected, of dimensionality nxe2x88x921.
The procedure based on scanning over a succession of hyper-surfaces is readily applicable to a search space of any dimensionality and becomes increasingly advantageous as the number of dimensions in the search space increases, both in terms of speed of finding the signal and ease of implementation relative to manual or other intuition-based alignment schemes.
For example, application of the procedure to a six-dimensional search space, as would be represented by alignment involving two xyz-positioners (x1,y1,z1,x2,y2,z2) is straightforward. Moreover, application of the procedure to angular axes of freedom, so-called xcex8-axes or xcfx86-axes, is no different than application to linear degrees of freedom. In fact, the one-to-one mapping between the degrees of freedom in real space and the dimensions in the hyper-space is totally arbitrary so that the same six-dimensional hyper-space can be used for defining a search pattern for driving an xyzxcex8-positioner and xy-positioner (x1,y1,z1,xcex81,x2,y2) as for the previously-mentioned example of two xyz-positioners (x1,y1,z1,x2,y2,z2). Moreover, for the same reason, any permutation of the one-to-one mapping between the real-space axes and the hyper-space axes will be equivalent. This allows simplification of the construction and operation of appropriate positioner control systems, since, of the n control signal output leads for driving a positioning element in each of the n positioning axes, any one of the output leads can be connected to any one of the positioning elements without affecting performance.
The use of hyper-cubes as the hyper-surfaces is numerically convenient. However, hyper-spheres, or hyper-surfaces of innumerable different topologies may be used instead. Examples of possible hyper-surface, topologies are cubic or cuboid, and spherical or ellipsoid. Especially if some or all of the positioning axes are linear, it is numerically convenient, and also convenient for the control signals, if the hyper-surface is of a shape having at least some cuboid side portions, for example the above-mentioned cubic or cuboid shape, or some other shape.
In an embodiment of the invention, the hyper-surface is topologically equivalent to a hyper-sphere and is expanded incrementally until the signal is located, so that the search procedure scans through a series of hyper-surfaces, each hyper-surface being topologically equivalent to a hyper-sphere and having a radius incrementally larger than the previous hyper-sphere in the series. At any increment step during the search, the search space is thus divided between an inner, searched sub-space and an outer, unsearched sub-space with the hyper-sphere expanding in the manner of a bubble in a quasi-continuous stepwise manner.
For many applications, the hyper-surfaces will be fully enclosed, reflecting a gaussian signal location probability in each dimension of the search space. However, in some applications, there may be a gaussian distribution in some, but not all, of the dimensions of the search space. For example, in a four-dimensional search space, the signal location distribution may be gaussian in only two dimensions in which case the hyper-surfaces can be chosen to be enclosed only in respect of those two dimensions. Such an anisotropic distribution could result from a laser slab mode or semiconductor diode laser output.
The invention has several different aspects, as are exemplified by the attached claims.
One field of application of the invention is in optics to find an optical signal. Within that field, one important group of applications relates to alignment procedures involving optical components such as optical fibers, solid-state waveguides, lasers and related system components, for example in the telecommunications field.